Question: Solve for $r$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $35r-21 < -35r + 19$
Solution: $\begin{aligned}35r-21 & < -35r + 19 \\\\ 35r&< -35r+40 &(\text{Add } 21 \text{ to both sides}) \\\\ 70r &< 40 &(\text{Add } 35r \text{ to both sides})\\\\ r&<\dfrac{4}{7}&(\text{Divide both sides by }70 \text{ and simplify}) \end{aligned}$ In conclusion, the answer is $r < \dfrac{4}{7}$.